Origin of Particle Masses from Quantum Geometric Modulation of the Higgs Mechanism

Here, we demonstrate that particle masses in the Standard Model emerge from quantum geometric modulation of the Higgs mechanism through a scalar field $\Pi$ with quantum rigidity $N \approx 43$. The field $\Pi$ modulates both the Higgs vacuum expectation value and Yukawa couplings, generating the observed lepton mass hierarchy. We predict electron mass $m_e = 0.5114$ MeV (0.08% error), muon mass $m_\mu = 105.59$ MeV (0.10% error), and tau mass $m_\tau = 1774.3$ MeV (0.15% error), with mass ratios accurate to 99.8%. The suppression factors emerge naturally from $N \approx 43$ through $\beta_f = N/k_f$, providing a geometric origin for the mass hierarchy. We derive testable predictions for LHC Higgs coupling measurements and cosmological mass variation constraints.